The dominant role of critical valence fluctuations on high T_c superconductivity in heavy fermions

Despite almost 40 years of research, the origin of heavy-fermion superconductivity is still strongly debated. Especially, the pressureinduced enhancement of superconductivity in CeCu2Si2 away from the magnetic breakdown is not sufficiently taken into consideration. As recently reported in CeCu2Si2 and several related compounds, optimal superconductivity occurs at the pressure of a valence crossover, which arises from a virtual critical end point at negative temperature Tcr. In this context, we did a meticulous analysis of a vast set of top-quality high-pressure electrical resistivity data of several Ce-based heavy fermion compounds. The key novelty is the salient correlation between the superconducting transition temperature Tc and the valence instability parameter Tcr, which is in line with theory of enhanced valence fluctuations. Moreover, it is found that, in the pressure region of superconductivity, electrical resistivity is governed by the valence crossover, which most often manifests in scaling behavior. We develop the new idea that the optimum superconducting Tc of a given sample is mainly controlled by the compound's Tcr and limited by non-magnetic disorder. In this regard, the present study provides compelling evidence for the crucial role of critical valence fluctuations in the formation of Cooper pairs in Ce-based heavy fermion superconductors besides the contribution of spin fluctuations near magnetic quantum critical points, and corroborates a plausible superconducting mechanism in strongly correlated electron systems in general